Plot Crack tip plastic zone shapes estimated from the elastic solution and the von

Mises yield criterion.

For Plane Stress, $\frac{r_y()}{\frac{1}{}[\frac{K_{\text{I}}}{{}_{ys}}{]}^2}=\frac{1}{4}[1+cos+\frac{3}{2}si{n}^2]$

For Plane Strain, $\frac{r_y()}{\frac{1}{}[\frac{K_{\text{I}}}{{}_{ys}}{]}^2}=\frac{1}{4}[(1-2v{)}^2(1+cos)+\frac{3}{2}si{n}^2],v=\frac{1}{3}$